Question

measurement and geometry continued

1. determine the values of angles \\(x\\) and \\(y\\).

Explanation:

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</pre_analysis>

<reasoning>

Calculate the interior angle \(y\) of the regular pentagon

\[

$$\begin{aligned} n &= 5 \\ y &= \frac{(n - 2) \times 180^\circ}{n} \\ y &= \frac{(5 - 2) \times 180^\circ}{5} \\ y &= \frac{3 \times 180^\circ}{5} \\ y &= 108^\circ \end{aligned}$$

\]

Calculate the exterior angle \(x\)

\[

$$\begin{aligned} x &= 180^\circ - y \\ x &= 180^\circ - 108^\circ \\ x &= 72^\circ \end{aligned}$$

\]
</reasoning>

<answer>
\(x = 72^\circ\), \(y = 108^\circ\)
</answer>

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"Mathematics",
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]
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</post_analysis>

Answer:

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],
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"Interior and Exterior Angles"
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</pre_analysis>

<reasoning>

Calculate the interior angle \(y\) of the regular pentagon

\[

$$\begin{aligned} n &= 5 \\ y &= \frac{(n - 2) \times 180^\circ}{n} \\ y &= \frac{(5 - 2) \times 180^\circ}{5} \\ y &= \frac{3 \times 180^\circ}{5} \\ y &= 108^\circ \end{aligned}$$

\]

Calculate the exterior angle \(x\)

\[

$$\begin{aligned} x &= 180^\circ - y \\ x &= 180^\circ - 108^\circ \\ x &= 72^\circ \end{aligned}$$

\]
</reasoning>

<answer>
\(x = 72^\circ\), \(y = 108^\circ\)
</answer>

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"Mathematics",
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"Regular Polygon Angles"
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